2 E Standard Model: the LHC reach · Christophe Grojean Beyond the Standard Model: the LHC reach...

E = mc2

Rµ! ! 12Rgµ! = 16!G Tµ!

E = h!

( [email protected] )

Ch!"o#e GrojeanCERN-TH & CEA-Saclay/IPhT

Beyond the Standard Model:the LHC reach

XIV Frascati Spring School “Bruno Touschek”

Christophe Grojean Beyond the Standard Model: the LHC reach Frascati, May '09

Conclusions Why do we expect to find a Higgs?

new particles/symmetries are expected to populate the TeV scale to trigger the breaking of the EW symmetry

1. discovery already announced to journalists and politics2. simplest parametrization of EWSB3. unitarity of WW scattering amplitude4. EW precision tests

Why do we expect more than the Higgs?1. dark matter and matter-antimatter asymmetry2. triviality3. stability4. naturality

new physics might be heavy if the Higgs is light

new physics has to be light if the Higgs is light

}!

what is the organization principle that governs this new sector?

new physics not necessarily coupled to SM


The Higgs mechanism is a description of EWSB. It is not an explanation. No dynamics to explain the instability at the origin.

Higgs Mechanism: a model without dynamics

Why is EW symmetry broken ? Because µ2 is negative

Why is µ2 negative ?

Because otherwise, EW symmetry won’t be broken

V (h) =12µ2h2 +

14!h4


Which Higgs?

UnHiggs?

Fat Higgs?

Portal Higgs?

Private Higgs?

Gaugephobic Higgs?

Higgsless?

Composite Higgs?

Gauge-Higgs? Lone Higgs?

Phantom Higgs?

Little Higgs?

Slim Higgs?Littlest Higgs?

Simplest Higgs?

Twin Higgs?

Intermediate Higgs?

Peter’s Higgs?Brout-Englert’s Higgs?

Guralnik’s Higgs?

Kibble’s Higgs?


Symmet!$ for a natural EWSB


How to Stabilize the Higgs Potential

spontaneously broken global symmetry massless scalar

a particle of spin s:2s+1 polarization states

...with the only exception of a particle moving at the

speed of light

... fewer polarization states

... but the Higgs has sizable non-derivative couplings

... but the Higgs is a spin 0 particle

m=0!Spin 1 Gauge invariance no longitudinal polarization!

!Chiral symmetry only one helicity!Spin 1/2

Goldstone’s Theorem

The spin trick


Symmetries to Stabilize a Scalar Potential

Supersymmetry

fermion ~ boson

Higher Dimensional

Lorentz invariance

4D spin 1 4D spin 0

Aµ ! A5

These symmetries cannot be exact symmetry of the Nature. They have to be broken. We want to look for a soft breaking in

order to preserve the stabilization of the weak scale.

gauge-Higgs unification models"

[Manton ’79, Fairlie 79, Hosotani ’83 +...]


Ghost symmetry

SM particle ~ ghost

It was known since Pauli-Villars that ghosts can soften the UV behavior of the propagators. But they are unstable per se.

Lee-Wick in the 60’s proposed a trick to stabilize the ghosts (at the price of of a violation of causality at the microscopic scale).

[Grinstein, O’Connell, Wise ‘07]

Other symmetries?


Li%le Hi&s


Little Higgs ModelsHiggs as a pseudo-Nambu-Goldstone boson

QCD: !+, !0 are Goldstone associated toSU(2)L ! SU(2)R

SU(2)isospin

!em ! 0, mq ! 0

LxR exact

m! = 0

!em != 0

m2

!± !

!em

4"

!2

QCD

EW pions!top ! 0, g, g

!! 0

exact global sym.

mH = 0

!top != 0

m2H !

!top

4"

!2strong ...too low !

Little Higgs = PNGB + Collective Breaking

m2H !

!i!j

(4")2!2

strong

[Arkani-Hamed et al. ‘02]

would require

!strong ! 1 TeV


Little Higgs = PNGB + Collective Breaking

Higgs!∈ G/HThe coset structure is broken by 2 sets of interactions

L = LG/H + g1L1 + g2L2

each interaction preserves a subset of the symmetryHiggs remains an exact PNGB when either g1 or g2 is vanishing

if gL or gR vanishes, SU(3)/SU(2) global sym. and Higgs remains massless

gauge SU(2)LxSU(2)R subgroup (broken to SU(2)D)

14-3=11 PNGB left = 31, 21/2, 10

SU(5)/SO(5)

24-10=14 PNGBlitt

lest Higgs

Higgs?


LH = !2 cancelled by same spin partner

h h

W± Z

g2

h h

W± ZH H

-g2

gauge boson loops cancelled by heavy gauge boson loops

y y

t

t, T

h h

x

!

y

2f

yf

T T

h h

top loop cancelled by heavy toop loop

Relation among different couplings follows from global sym.

cancellation of div. occurs only at one-loop


New particles (W’, Z’,top’...)

UV completion

SM particles (Higgs,W,Z...)100 GeV

1 TeV

10 TeV

v ! f/4!

f

4!f

cancellation of Higgs mass !2 divergences

Anatomy of Little Higgs models

W,Z loop cancelled by heavy W’, Z’ loops

top loop cancelled by heavy top' loop

Higgs loop cancelled by heavy scalar loops


Little Higgs @ LHC

Confrontation of Little Higgs with EW data: needs for a T-parity

light particles = even ⇔ heavy particles = odd

the Lightest T-odd Particle (usually partner of Bµ) is stable (DM?)

Little Higgs = jet+ missing ET

• The Lightest T-Odd Particle (LTP) is stable, typically the neutral, spin-1 “heavy photon” - WIMP DM candidate

• Symmetry structure forces introduction of T-odd partners for each SM (weak doublet) fermion - “T-quarks” and “T-leptons”

• Hadron collider signature: T-quark production, decays to LTP+jets

LHT Collider Phenomenology

T-odd Quarks Mass (GeV)

0 100 200 300 400 500

Ma

ss

(G

eV

)H

B

0

50

100

150

200

250

300

350

400

450

500

DØ only-1Tevatron 0.31 fb

= Qµ/exp. , -1Tevatron 8 fb

LEP squark searches

T-odd Quarks Mass (GeV)200 400 600 800 1000 1200 1400


Cro

ss s

ecti

on

(p

b)

-210

-110

1

10

210

Tevatron

LHC

[Carena, Hubisz, MP, Verdier, hep-ph/0610156]

Another “SUSY look-alike” candidate!

• The Lightest T-Odd Particle (LTP) is stable, typically the neutral, spin-1 “heavy photon” - WIMP DM candidate

• Symmetry structure forces introduction of T-odd partners for each SM (weak doublet) fermion - “T-quarks” and “T-leptons”

• Hadron collider signature: T-quark production, decays to LTP+jets

LHT Collider Phenomenology

T-odd Quarks Mass (GeV)

0 100 200 300 400 500

Mass (

GeV

)H

B

0

50

100

150

200

250

300

350

400

450

500

DØ only-1Tevatron 0.31 fb

= Qµ/exp. , -1Tevatron 8 fb

LEP squark searches



Cro

ss

se

cti

on

(p

b)

-210

-110

1

10

210

Tevatron

LHC

[Carena, Hubisz, MP, Verdier, hep-ph/0610156]

Another “SUSY look-alike” candidate![Carena, Hubisz, Perelstein, Verdier ‘07]

Interesting physics also associated to top partner (pair production: gg # TT)


Test of Little Higgs Structure

Little Higgs models require a heavy top and heavy gauge bosons

to guarantee the cancellation of the !2 divergences, the couplings of the new gauge bosons to the SM fermions are fixed

production cross section of heavy WH and ZH

Burdman, Perelstein, Pierce ‘02Partial width of ZH to fermions

is proportional to cotan2!

Partial width of ZH into boson pairs(Zh and W+W-)

is proportional to cotan2 2!(this follows from the particular coupling of the

Higgs to the two SU(2) gauge groups)

cotan !=g1/g2 (two SU(2) gauge couplings)

100 fb (three years of LHC)

WHWH

±3

h

W+µL

W!!L

igMW!µ! h

W+µH

W!!H

!igMW!µ!

h

W±µH

W"!L

!igMW cot 2" !µ!

FIG. 2. Cubic couplings between the physical Higgs bosonh and pairs of charged gauge bosons.

other rotations required to diagonalize the mass matrixinvolve angles of order #; we will not need to know themexplicitly. The Higgs couplings to pairs of gauge bosonsare proportional to the elements of the matrix M2; wecollect the non-vanishing couplings in Fig. 1, keeping onlythe leading order in #. Note that M2 is not diagonal inthe mass eigenbasis, leading to o!-diagonal Higgs cou-plings such as W 3

HZh. The cubic couplings of the Higgsto charged gauge bosons are computed in the same fash-ion; they are shown in Fig. 2.

The three diagonal couplings of the Higgs in Fig. 1,hZZ, hW 3

HW 3H and hBHBH , add up to zero. So do the

two diagonal couplings in Fig. 2, hW+L W!

L and hW+H W!

H .These cancellations can be traced back to Eq. (10), andare therefore directly related to the crucial cancellationof quadratic divergences. Measuring the diagonal cou-plings would provide the most direct way to verify thelittle Higgs model. Unfortunately, experimentally this isa di"cult task: the measurement requires associated pro-duction of a WH boson with a Higgs. The cross sectionfor this process is very small: with 100 fb!1 integratedluminosity at the LHC there are typically only tens ofevents in this channel, rendering it virtually unobservableonce specific final states are considered. It is much eas-ier to measure the o!-diagonal couplings, such as hW 3

HZand hW±

H W"L . Although these couplings do not directly

participate in the cancellation of quadratic divergences,verifying their structure would provide a strong evidencefor the crucial feature of the model, Eq. (9). Indeed, thefactor of cot 2" in these couplings is a unique consequenceof Eq. (9). To illustrate this point, consider an alterna-tive “big Higgs” theory with the same [SU(2) " U(1)]2

gauge structure as the little Higgs, but with a Higgs fieldtransforming only under a single SU(2) " U(1) factorwith SM quantum numbers. (The one-loop quadratic di-vergence in the Higgs mass parameter is not canceled inthis theory.) This theory predicts hW 3

HZ and hW±H W"

Lvertices of the same form as in the little Higgs model,but with the replacement cot 2" # cot". Thus, if themixing angle " can be obtained independently, the mea-surement of these vertices would act as a discriminatorbetween the little Higgs and the alternative theory.

Production and decay of heavy gauge bosons — Heavygauge bosons W a

H and BH are produced at the LHC

predominantly through their coupling to quarks. Thecharges of the SM fermions under the extended [SU(2)"U(1)]2 gauge group are constrained by the requirementthat they have correct transformation properties underits low-energy subgroup. We choose the left-handedfermions to transform as doublets under SU(2)1 and sin-glets under SU(2)2; the right-handed fermions are sin-glets under both SU(2)’s [4]. The couplings of the heavySU(2) bosons have the form

g cot" W aHµ

!

L$µ %a

2L + Q$µ %a

2Q

"

, (12)

where L and Q are the left-handed lepton and quarkfields, and we suppress the generation indices. Thecharges of the fermions under the two U(1) groups haveto add up to the SM hypercharge, Q1 + Q2 = Y , but areotherwise unconstrained. This implies a high degree ofmodel-dependence in the couplings of the BH boson tofermions. Note that the strongest electroweak precisionconstraints on the little Higgs model [3,5] arise preciselyfrom the diagrams involving the BH . Certain choices ofthe fermion charges and the angle "# can help minimizethese constraints [6]; alternately, the extra U(1) can beeliminated completely [9] without introducing significantfine tuning due to the smallness of the coupling g#. Giventhis model uncertainty in the U(1) sector, we will con-centrate on the production and decay of the SU(2) heavybosons.

In pp collisions at the LHC, the heavy gauge bosons arepredominantly produced through qq annihilation. Thesub-process qg # WHq is considerably smaller and couldbe separately identified due to the presence of a highpT jet. Fig. 3 shows the leading order production crosssection of WH as a function of its mass, for the case" = &/4. The general case may be obtained from Fig.by simply scaling by cot2 ".

FIG. 3. Production cross sections for W 3H (solid) and W±

H

(dashed) at the LHC, for ! = "/4. We use the CTEQ5Lparton distribution function.

From our discussion thus far, it is clear that the two-body decay channels of the W 3

H include W 3H # ff , where

3


Gau'-Hi&s Unification


How to Get a Doublet from an Adjoint

Consider a 5D gauge symmetry G

H ! Aa

5 will belong tho the adjoint rep. of G

The SM Higgs is not an adjoint of SU(2)xU(1), it is a doublet !

Consider a bigger gauge group

G ! SU(2)l " U(1)y

Adj doublet + other rep.

Adj1

2

!

"

"

"

"

#

W3 + W8/!

3 W1 " iW2 W4 " iW5

W1 + iW2 "W3 + W8/!

3 W6 " iW7

W4 + iW5 W6 + iW7 "2W8/!

3

$

%

%

%

%

&

SU(3)SU(2)xU(1)

2!3/2


wavefunction =localization of KK mode

along the xdim

Compactification on a Circle

Towards a Complete Construction

so far we haven’t broken any symmetry... we even enlarged the gauge group

We need to break G down to SU(2)xU(1)

we can achieve this breaking while compactifying the extra-dimension

!(y + 2"R) = !(y)circle:

y ! y + 2!R

!R

!!R

0

y

!(x, y) =!

n

1!2!n0"R

"cos

"ny

R

#!+

n (x) + sin"ny

R

#!!n (x)

#

5D field

4D Kaluza-Klein modes

mn = pny =

n

R


Compactification on an Orbifold

y ! y + 2!R

!R

!!R

0

Towards a Complete Construction

so far we haven’t broken any symmetry... we even enlarged the gauge group

We need to break G down to SU(2)xU(1)

we can achieve this breaking while compactifying the extra-dimension

y

!(y + 2"R) = !(y)Z2

!

!

!y

y ! "yorbifold:

U2

= 1!(!y) = U!(y)

circle:

U=+1: cos!ny

R

"wavefunctions

E

massless mode

U=-1: sin!ny

R

"wavefunctions

E

massless mode


!R

!!R

0

Orbifold breaking

Z2

y ! "yorbifold

!

!

y

!y

Aµ(!y) = UAµ(y)U†

A5(!y) = !UA5(y)U†

U2

= 1

0 " R

Aµ(0) = UAµ(0)U†Breaking of gauge group at the end-points of the orbifold

at the end-points, the surviving gauge group commute with the orbifold projection matrix U

KK effective theoryzero mode: is independent of Aµ y

Aµ = UAµU†

A5 = !UA5U†

GH0 H0

gauge symmetry breaking(+ chiral fermions)


SU(3) ! SU(2)xU(1) 5D Orbifold Breaking

U =

!

"

!1

!1

1

#

$ U ! SU(3) U2

= 1

massless vectors Aµ

[Aµ, U ] = 0 Aµ =1

2

!

"

"

"

"

#

A3µ + A8/

!

3 A1µ " iA2

µ

A1µ + iA2

µ "A3µ + A8

µ/!

3

"2A8µ/

!

3

$

%

%

%

%

&

SU(2) ! U(1)

massless scalars A5

{A5, U} = 0 A5 =1

2

!

"

"

"

"

#

A45 ! iA5

5

A65 ! iA7

5

A45 + iA5

5 A65 + iA7

5

$

%

%

%

%

&

SU(3)

SU(2) ! U(1)


Orbifold Projection as Boundary Conditions

G ! H by orbifold projection

!R

!!R

0

!

!Z2

y

!yU

2= 1 BC BC!

which is equivalent to the BCsat the fixed points

!5AHµ = 0

AH5 = 0

AHµ (!y) = AH

µ (y)

AH5 (!y) = !AH

5 (y)

H subgroup

AG/Hµ (!y) = !A

G/Hµ (y)

AG/H5

(!y) = AG/H5

(y)

which is equivalent to the BCsat the fixed points

AG/Hµ = 0

!5AG/H5

= 0

G/H coset


Wave-functions for flat space Z2xZ’2 orbifoldassuming Z and Z’ commute

cosny

Rmn =

n

Rn = 0 . . .!"(+,+) states:

sinny

Rmn =

n

Rn = 1 . . .!"(-,-) states:

cos(2n + 1)y

2Rmn =

2n + 12R

n = 0 . . .!"(+,-) states:

sin(2n + 1)y

2Rmn =

2n + 12R

n = 0 . . .!"(-,+) states:

KK towerwith a

massless mode

"(+,+) states: cosny

Rmn =

n

Rn = 0 . . .!


Two examples

0 " R

SU(3)SU(2)xU(1) SU(2)xU(1)

: SU(2)xU(1) : SU(3)/SU(2)xU(1)µ(+,+)(-,-)5

µ(-,-)(+,+)5

0 " R

S0(5)xU(1)X

SU(2)LxU(1)Y SO(4)xU(1)X

: : : SO(5)/SO(4)SU(2)LxU(1)YSO(4)xU(1)X

SU(2)LxU(1)Y

µ(+,+)(-,-)5

µ(-,-)(+,+)5

µ(-,+)(+,-)5

massless Higgs doublet

massless Higgs doublet


Experimental Signatures

the collider signals haven’t been studied in details (lack of fully realistic models?)

the main predictions of these models are

KK excitations of W,Z around 500 GeV ~ 1 TeV

KK excitations of G/H: gauge bosons with the quantum numbers of the Higgs doublets

extra fermions (to cancel the top loop quadratic divergence)


new particles/symmetries that populate the TeV scale to stabilize the EW scale and suppress dangerous !2 quantum corrections

to the Higgs mass

Little Higgs, gauge-Higgs unification:two concrete classes of models with

what is canceling the infamous divergent diagrams?

h

W± Z top

h

h

h h

h h

Models designed to address the question:


But this is assuming that we already know the answer to the central question of EW symmetry breaking

what is unitarizing the WW scattering amplitude?

L

L

L

L

A = g2

!

E

MW

"2

A finite

Higgsless models & composite Higgs

other way to unitarize the WW amplitude:


Weakly coupled models Strongly coupled models

prototype: Susy

TeVQCD

prototype: Technicolorsusy partners ~ 100 GeV rho meson ~ 1 TeV

other ways?

what is unitarizing the WW scattering amplitude?

What is the mechanism of EWSB?


Strongly coupled models

The resonance that unitarizes the WW scattering amplitudes

generates a tree-level effect on the SM gauge bosons self-energy

a phenomenological challenge: how to evade EW precision data

+ ...=TC

a theoretical challenge: need to develop tools to do computation

parameter of orderS m2W /m2

!

In conflict with EW precision data from LEP

|S| < 10!3( exp: @ 95% CL)


Back to “Technicolor” from Xdims

Warped gravity with fermions and gauge field in the bulk

and Higgs on the brane

Strongly coupled theorywith slowly-running couplings in 4D

UV IR

G

H

H

H0 5D

motion along 5th dim

UV brane

IR brane

bulk local sym.

4D

RG flow

UV cutoff

break. of conformal inv.

global sym.Advantages

hierarchy problem addressed + gauge coupling unification

weakly coupled description ! calculable models

new approach to fermion embedding and flavor problem

A5 ! A5 + !5" h ! h + apseudo-Goldstone of a strong force

“AdS/CFT” correspondence for model-builder

KK modes vector resonances (!mesons in QCD)


Hi&sl$s Models


Higgsless Approach

Gauge symmetry breaking

In the gauge-Higgs unification models, we have been breaking bigger gauge groups down to SU(2)xU(1) by orbifold.

Why can’t we break directly SU(2)xU(1) to U(1)em by orbifold?

Let us try...

!R

!!R

0

!

!Z2

y

!yU

2= 1

Csaki, Grojean, Murayama, Pilo, Terning ‘03Csaki, Grojean, Pilo, Terning ‘03


quantum mechanics in a box

Higgsless Models

boundary conditions generate a transverse momentum

Is it better to generate a transverse momentum than introducing by hand a symmetry breaking mass for the gauge fields?

ie how is unitarity restored without a Higgs field?

m2= E2

! !p32! !p!

2

momentum along extra dimensions ~!4D mass

mass without a Higgs


Unitarization of (Elastic) Scattering AmplitudeSame KK mode

‘in’ and ‘out’ !µ

!=

! |"p|

M,

E "p

M |"p|

"

A = A(4)

!

E

M

"4

+ A(2)

!

E

M

"2

+ . . .

n

k

n

n n

s channel exchange

contact interaction

A = A(4)

!E

M

"4

+ A(2)

!E

M

"2

+ . . .

!µ! =

# |"p|M

,E "p

M |"p|

$

1

n

k

n

n n

s channel exchange

n n

n n

contact interaction

A = A(4)

!E

M

"4

+ A(2)

!E

M

"2

+ . . .

!µ! =

# |"p|M

,E "p

M |"p|

$

1

n n

k

n n

t channel exchange

n

k

n n

n

u channel exchange

M! = 0

MW± =1

2R

MZ =1

R

A3µ(x, y) =

!!

k=0

"2

2"k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

2

n n

k

n n

t channel exchange

n

k

n n

n

u channel exchange

M! = 0

MW± =1

2R

MZ =1

R

A3µ(x, y) =

!!

k=0

"2

2"k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

2

gnnkg2

nnnn gnnk

gnnk gnnk

gnnkgnnk

!!p

!q!p

!q

A(4) = i

!

g2nnnn !

"

k

g2nnk

#

$

fabefcde(3 + 6c! ! c2!) + 2(3 ! c2

!)facef bde

%

A(2)= i

!

4g2nnnn ! 3

"

k

g2nnk

M2k

M2n

#

$

facef bde ! s2!/2f

abefcde%


KK Sum Rules

A(4) ! g2nnnn "

!

k

g2nnk A(2) ! 4g2

nnnn " 3!

k

g2nnk

M2k

M2n

E4 Sum Rule

g2nnnn !

!k

g2nnk = g2

5D

" !R

0

dyf4n(y) ! g2

5D

" !R

0

dy

" !R

0

dzf2n(y)f2

n(z)!

k

fk(y)fk(z) = 0

!

k

fk(y)fk(z) = !(y ! z)

Completness of KK modesA(4)

= 0

In a KK theory, the effective couplings are given by overlap integrals of the wavefunctions

gmnp = g5D

! !R

0

dyfm(y)fn(y)fp(y)g2

mnpq = g2

5D

! !R

0

dyfm(y)fn(y)fp(y)fq(y)contact interaction

A1,2µ = 0

!!A3µ = 0

Tr (UF56(0)) ! Tr (Ug(0)F56(0)g"1(0)) = Tr (UF56(0)g"1(0)g(0)) = Tr (UF56(0))

Veff(A5) = f(Wn)

Wn = eiR 2n!R0 A5dy

fHHH , fG/H G/H H

[H, H ] " H [H, G/H ] " G/H

"AG/Hµ = 0

"AG/H5 = !5#

G/H + gfG/H G/H HAG/H5 #H

7

s channel exchange

A3µ(x, y) =

!!

k=0

"2

2!k0!Rcos

ky

R"(k)

µ (x)

A1µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+(k)

µ (x) + W" (k)µ (x)

$

A2µ(x, y) =

!!

k=0

1!!R

sin(2k + 1)y

2R

#W+ (k)

µ (x) " W" (k)µ (x)

$

f = 0 or f # = 0 at y = 0, !R

f ##n(y) = "m2

nfn(y)

Aµ(x, y) =!

n

fn(y)Anµ(x)

!4Aaµ " #2

5Aaµ = 0

6

Csaki, Grojean, Murayama, Pilo, Terning ‘03


{Warped Higgsless Model

Csaki, Grojean, Pilo, Terning ‘03

SU(2)LxSU(2)R

xU(1)B-L

U(1)em

SU(2)LxU(1)y U(1)B-LxSU(2)D

AR±µ = 0

g!5Bµ ! g5AR 3µ = 0

!5(g5Bµ + g!5AR 3µ ) = 0

AL aµ ! AR a

µ = 0

!5(AL aµ + AR a

µ ) = 0

UV brane IR brane

! =RIR

RUV

! 1016

GeV

ds2=

!

R

z

"2#

!µ!dxµdx!! dz2

$

z = RUV ~ 1/MPl z = RIR ~ 1/TeV

log suppression!

!

“light” mode: M2

W =1

R2

IRlog(RIR/RUV )

M2

Z !

g25 + 2g!25g25

+ g!21

R2IR

log(RIR/RUV )

KK tower: M2

KK =cst of order unity

R2

IR

BCs kill all A5 massless modes: no 4D scalar mode in the spectrum


Postponing Pert. Unitarity Breakdown

Is it a counter-example of the theorem by Cornwall et al.?i.e. can we unitarize the theory without scalar field?

No! g2

nnnn =!

k

g2

nnk =!

g2

nnk

3M2

k

4M2n

E4 E2

the sum rules cannot be satisfied with a finite number of KK modes (to unitarize the scattering of massive KK modes, you always need heavier KK states)

Pushing the need for a scalar to higher scaleWith a finite number of KK modes

MW

MW !

MW !!

MW (n)

4!MW /g4Naive cutoff

4!MW (n)/g45D

cutoff

New Physics (Higgs/strongly coupled theory?) { not directly set by the weak scale

flat space

a factor 15 higher than the naive 4D cutoffthanks to the non-trivial KK dynamics

!5D = 24!3/g25 = (3!/g4) !4D

g4 = g5/!

2!R MW = 1/R( )&


SM Fermions in Higgsless Models

SU(2)LxSU(2)R

xU(1)B-LSU(2)Lx U(1)y SU(2)DxU(1)B-L

vector-like braneisospin invariant mass only

(same mass for the top and bottom or electron and neutrino)

Chiral braneno possible mass term

The fermions have to live in the bulk


a narrow and light resonance

Collider Signaturesunitarity restored by vector resonances whose masses and

couplings are constrained by the unitarity sum rules

WZ elastic cross section

Birkedal, Matchev, Perelstein ’05He et al. ‘07

gWW !Z !gWWZM2

Z"3MW !MW

!(W !! WZ) "

!M3W !

144s2wM2

W

550 GeV ! 10 fb!1

1 TeV ! 60 fb!1

Number of events at the LHC, 300 fb-1

discovery reach @ LHC

(10 events)

W’ production

should be seen within one/two year

q

q

Z0

W±

W’Z0

q

q

W±

VBF (LO) dominates over DY since

couplings of q to W’ are reduced

2j+3l+ET

no resonance in WZ for SM/MSSM

2 E Standard Model: the LHC reach · Christophe Grojean Beyond the Standard Model: the LHC reach...

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Transcript of 2 E Standard Model: the LHC reach · Christophe Grojean Beyond the Standard Model: the LHC reach...